Cremona's table of elliptic curves

975 = 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	975g	Isogeny class
Conductor	975	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	16453125 = 34 · 56 · 13	Discriminant
Eigenvalues	-1 3- 5+  4  4 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1738,-28033]	[a1,a2,a3,a4,a6]
j	37159393753/1053	j-invariant
L	1.4788241842231	L(r)(E,1)/r!
Ω	0.73941209211155	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15600be4 62400bf4 2925f4 39a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975g3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	-	+	4	4	+	-2	0	0	-10	4	2	6	12	0	-6	12	-2	8	0	-2	8	-4	-2	-10

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Quadratic twists for elliptic curve 975g3

-4	8	-3	5	-7	-11	13
15600be4	62400bf4	2925f4	39a2	47775u4	117975by4	12675w3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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